Answer:
5
Step-by-step explanation:
slope = (8-0)/(4-(-2))
= 8/6
= 4/3
y = 4/3 x + c
0 = -8/3 + c
c = 8/3
y = 4/3x + 8/3
To find the distance, we have to find a line perpendicular to the above line, which also passes through P(5,1).
This can be done by making it such that both slopes give a product of -1.
y = -3/4x + c
Substituting (5,1):
1 = -15/4 + c
c = 19/4
y = -3/4x + 19/4
Now, to find the point where both these lines intersect, we use simultaneous linear equations:
-3/4x + 19/4 = 4/3x + 8/3
4/3x + 3/4x = 8/3 - 19/4
25/12x = -25/12
x = 1
Substituting x into 'y = -3/4x + 19/4':
-3/4 + 19/4 = 4
(1,4) is the point closest to P(5,1)
Finding the distance using the distnace formula:
[tex]\sqrt{(1-4)^2 + (5-1) ^2}\\\\= \sqrt{9 + 16}\\\\= \sqrt{25}\\\\= 5[/tex]
Hence, the distance is 5.
Feel free to mark this as brainliest! :D
